Consider the differential equation: y = 3y - 2x Using a pencil, graph the isoclines. Also, using a pen, graph the slope field, as well as three solutions satisfying each of the three conditions: y(0) = 0, y(0) = 1, y(0)=-1.
Consider the differential equation: y = 3y - 2x Using a pencil, graph the isoclines. Also, using a pen, graph the slope field, as well as three solutions satisfying each of the three conditions: y(0) = 0, y(0) = 1, y(0)=-1.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 16CR
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![Consider the differential equation:
y = 3y - 2x
Using a pencil, graph the isoclines. Also, using a pen, graph the slope field, as well as three
solutions satisfying each of the three conditions: y(0) = 0, y(0) = 1, y(0)=- 1.
3y-2X=1T => y = (2x +k)
3x
y = ²/3 x +ce ³*
for y(o) => C=0 => y = /2x
for y(o)=1
C= 1
ce
// (0) + (2²(0)
So, y = 2/x +e³x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F28e7be30-eca9-4147-a850-5833b744a665%2F86357a99-a911-45be-a228-88d1e66c1bd2%2Ff6qfzr9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the differential equation:
y = 3y - 2x
Using a pencil, graph the isoclines. Also, using a pen, graph the slope field, as well as three
solutions satisfying each of the three conditions: y(0) = 0, y(0) = 1, y(0)=- 1.
3y-2X=1T => y = (2x +k)
3x
y = ²/3 x +ce ³*
for y(o) => C=0 => y = /2x
for y(o)=1
C= 1
ce
// (0) + (2²(0)
So, y = 2/x +e³x
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